Band structure and omnidirectional photonic band gap in lamellar structures with left-handed materials

Abstract

We theoretically investigate the photonic band structure of one-dimensional superlattices composed of alternating layers of right-handed and left-handed materials (RHM and LHM). The dispersion curves are mainly studied by assuming that the dielectric permittivity and magnetic permeability are constant in each layer. It is shown that such structures can exhibit new types of electromagnetic modes and dispersion curves that do not exist in usual superlattices composed only of RHM. In particular, we emphasize the possibility of bands that originate from the interface modes localized at the boundary between a LHM and RHM or from confined modes in one type of layers. These waves are evanescent in both or in one constituent of the superlattice. One of the pass bands may lie below the light lines of the constituting material and go down to the static limit of a vanishing frequency omega, even at a value of the wave vector k(//) (parallel to the layers) that is different from zero. For a given value of the wave vector k(//), the dispersion curves omega versus k(z) (where k(z) is the Bloch wave vector of the periodic system along the axis of the superlattice) may exist only in a limited part of the superlattice Brillouin zone and exhibit a zigzag behavior instead of a monotonic behavior as in usual superlattices. With an appropriate choice of the parameters, we show that it is possible to realize an absolute (or omnidirectional) band gap for either transverse electric (TE) or transverse magnetic (TM) polarization of the electromagnetic waves. A combination of two multilayer structures composed of RHM and LHM is proposed to realize, in a certain range of frequency, an omnidirectional reflector of light for both polarizations.

Surface Optical Waves in Semi-Infinite One-Dimensional Photonic Crystals Containing Alternating Layers of Positive and Negative Media with a Cap Layer

“…is the lattice constant, and c is the light speed in vacuum [11]. It is well known that when any periodic system is limited, k should be complex…”

“…To the best of our knowledge, there is no report regards to the surface modes in L-R PC. Left handed materials in which the dielectric permittivity ε and magnetic permeability µ are simultaneously negative, have received a great deal of attention during the last few years [11]. In our calculations, the dielectric permittivity and magnetic permeability are, in general, assumed to take constant values.…”

Investigating Optical Properties of One-Dimensional Photonic Crystals Containing Semiconductor Quantum Wells

“…Alongside the geometrical parameters of the PCs, the constituent materials types used in the PC have a great impact on their band structure. Optical properties of the PCs of various types of materials such as metals, semiconductors, graphenes, and metamaterials are explored in previous studies [7][8][9][10]. However, PBGs in conventional dielectric PCs strongly depend on the polarization and incidence angle of the electromagnetic waves and this may differ in other types of PCs as well.…”

Band Structures and Abnormal Behavior of One Dimensional Photonic Crystal Containing Negative Index Materials

“…The zero-φ eff gap distinguishes itself from a Bragg gap in that it is invariant with a change of scale length and is insensitive to thickness fluctuation. Baria et al [18] have investigated the band structures of one-dimensional superlattices composed of right handed materials and left handed materials. It is shown that such structures can exhibit new type of electromagnetic modes and dispersion curve that do not exist in usual superlattices composed only by right handed materials.…”